For what it's worth, my Oz V'hadar Mesivta Haggadah, extended edition, does indeed include it in brackets (p. 57).
In their discussion of the Minhag (p. 309) they reference the Ma'aseh Rav (§190), which lists the passages which the Gra would say. As you note, he leaves out the passage from Ezra. They pose this question (ad. loc., ft. 4) in the name of several Achronim (R' Moshe Shapira quoting the Ohr Sameiach; the Aderet). They quote two answers (it's unclear from their wording who said which answer):
- The Gra doesn't hold that one should say Pesukim regarding the Karban Pesach in the Second Temple, since the Temple didn't have the same level of holiness as the First one (cf. Yoma 21b and 52b).
- Those Karbanos which Ezra brought were from animals taken from Daryavesh and his advisers; this was a Hora'as Sha'ah, since in general one may not buy animals from an idolater (cf. Avodah Zarah 22a). Since the purpose of saying Seder Karban Pesach is that our speech should substitute for actually bringing the Karbanos, we prefer to only discuss Karbanos brought in the ideal manner.